A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Approximating smooth planar curves by arc splines
Journal of Computational and Applied Mathematics
Approximation of an open polygonal curve with a minimum number of circular arcs and biarcs
Computational Geometry: Theory and Applications
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Optimal approximation of closed polygons differs from the case of open polygons in the sense that the location of a starting point must be determined in a suitable way. We present an algorithm which first computes a proper extremal arc as starting point and then approximates the input polygon with a minimum number of circular arcs and line segments. The resulting curve is called Cyclic Minimum Arc Path (CMAP). Our algorithm guarantees the CMAP staying inside a user-specified tolerance. In contrast to the existing approaches, we do not restrict the breakpoints of the arc spline to a predefined set of points but choose them automatically. This has considerable effects on the resulting number of segments. We can handle every type of tolerance zone representing the user-specified tolerance as long it is formed by piecewise restricted analytic curves. In case of polygonal tolerance zones the proposed algorithm takes O(n^3) time for an original polygonal chain with n vertices. For generating a solution which has at most one additional segment we present an O(n^2) algorithm.